Topology and its Applications最新文献_第10页

Spaces determined by countably many locally compact subspaces 由可数局部紧凑子空间决定的空间

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-05-28 DOI: 10.1016/j.topol.2024.108973

Jimmie Lawson , Xiaoquan Xu

{"title":"Spaces determined by countably many locally compact subspaces","authors":"Jimmie Lawson , Xiaoquan Xu","doi":"10.1016/j.topol.2024.108973","DOIUrl":"10.1016/j.topol.2024.108973","url":null,"abstract":"<div>The theory of compactly generated spaces, alternatively k-spaces, plays an important role in general and algebraic topology. In this paper, we develop a theory of compact generation for non-Hausdorff spaces using locally compact spaces. We are particularly interested in the case that countably many locally compact spaces suffice and restrict our attention to that case. The notion of <math><mi>ℓ</mi><msub><mrow><mi>c</mi></mrow><mrow><mi>ω</mi></mrow></msub></math>-spaces (which can be considered as a type of <math><msub><mrow><mi>k</mi></mrow><mrow><mi>ω</mi></mrow></msub></math>-spaces) is introduced, which are determined by countably many locally compact spaces. It is proved that the product space of two <math><mi>ℓ</mi><msub><mrow><mi>c</mi></mrow><mrow><mi>ω</mi></mrow></msub></math>-spaces is still an <math><mi>ℓ</mi><msub><mrow><mi>c</mi></mrow><mrow><mi>ω</mi></mrow></msub></math>-space. We slightly modify the notion of an <math><mi>ℓ</mi><msub><mrow><mi>c</mi></mrow><mrow><mi>ω</mi></mrow></msub></math>-space to apply it to posets equipped with the Scott topology. The notions of <math><mi>ℓ</mi><msub><mrow><mi>c</mi></mrow><mrow><mi>ω</mi></mrow></msub></math>-posets, <math><mi>ℓ</mi><msub><mrow><mi>f</mi></mrow><mrow><mi>ω</mi></mrow></msub></math>-posets and c-posets are introduced. We develop a corresponding theory for these three kinds of posets and investigate the conditions under which the Scott topology on the product of two posets is equal to the product of the individual Scott topologies and under which the Scott topology on a dcpo is sober. Several such conditions are given.</div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"354 ","pages":"Article 108973"},"PeriodicalIF":0.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141188597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Mosaics for immersed surface-links 浸入式表面连接马赛克

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-05-27 DOI: 10.1016/j.topol.2024.108961

Seonmi Choi , Jieon Kim

引用次数: 0

Retraction notice to “The decomposition uniqueness for infinite Cartesian products” [Topol. Appl. 230 (2017) 16–23] 无限笛卡尔积的分解唯一性》撤稿通知[Topol. Appl. 230 (2017) 16-23]

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-05-23 DOI: 10.1016/j.topol.2024.108942

Daria Michalik

引用次数: 0

Retraction notice to “Some remarks on the uniqueness of decomposition into Cartesian product” [Topol. Appl. 201 (2016) 2–12] 关于分解为笛卡尔积的唯一性的几点评论》的撤稿通知[Topol. Appl.

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-05-23 DOI: 10.1016/j.topol.2024.108941

Daria Michalik

引用次数: 0

Extension of unbounded uniformly continuous functions and pseudometrics 无界均匀连续函数的扩展和伪计量学

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-05-22 DOI: 10.1016/j.topol.2024.108959

Michal Hevessy

引用次数: 0

Note on quasisymmetric rigidity of carpets 关于地毯准对称刚性的说明

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-05-21 DOI: 10.1016/j.topol.2024.108960

Yahui Sheng , Chun Wei , Fan Wen

引用次数: 0

Homotopical characterization of strongly contextual simplicial distributions on cone spaces 圆锥空间上强上下文简约分布的同向表征

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-05-18 DOI: 10.1016/j.topol.2024.108956

Aziz Kharoof, Cihan Okay

引用次数: 0

On multiplicative spectral sequences for nerves and the free loop spaces 论神经和自由环空间的乘法谱序列

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-05-17 DOI: 10.1016/j.topol.2024.108958

Katsuhiko Kuribayashi

引用次数: 0

Ultra-pseudo metric spaces and their characterization with completely regular topological spaces 超伪度量空间及其与完全规则拓扑空间的表征

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-05-16 DOI: 10.1016/j.topol.2024.108955

Satya Narayan Shukla, Surabhi Tiwari

引用次数: 0

The Nielsen realization problem for non-orientable surfaces 不可定向曲面的尼尔森实现问题

IF 0.6 4区数学

Topology and its Applications Pub Date : 2024-05-16 DOI: 10.1016/j.topol.2024.108957

Nestor Colin , Miguel A. Xicoténcatl

{"title":"The Nielsen realization problem for non-orientable surfaces","authors":"Nestor Colin , Miguel A. Xicoténcatl","doi":"10.1016/j.topol.2024.108957","DOIUrl":"10.1016/j.topol.2024.108957","url":null,"abstract":"<div>We show the Teichmüller space of a non-orientable surface with marked points (considered as a Klein surface) can be identified with a subspace of the Teichmüller space of its orientable double cover. It is also well known that the mapping class group <math><mi>Mod</mi><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>;</mo><mi>k</mi><mo>)</mo></math> of a non-orientable surface can be identified with a subgroup of <math><mi>Mod</mi><mo>(</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>g</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>;</mo><mn>2</mn><mi>k</mi><mo>)</mo></math>, the mapping class group of its orientable double cover. These facts, together with the classical Nielsen realization theorem, are used to prove that every finite subgroup of <math><mi>Mod</mi><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>;</mo><mi>k</mi><mo>)</mo></math> can be lifted isomorphically to a subgroup of the group of diffeomorphisms <math><mi>Diff</mi><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>;</mo><mi>k</mi><mo>)</mo></math>. In contrast, we show the projection <math><mi>Diff</mi><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>)</mo><mo>→</mo><mi>Mod</mi><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>)</mo></math> does not admit a section for large g.</div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"353 ","pages":"Article 108957"},"PeriodicalIF":0.6,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0